Optimization of the Individual Stiffness and Damping Parameters in Multiple-Tuned-Mass-Damper Systems

Abstract

The characteristics of multiple tuned-mass-dampers (MTMDs) attached to a single-degree-of-freedom primary system have been examined by many researchers. Several papers have included some parameter optimization, all based on restrictive assumptions. In this paper, we propose an efficient numerical algorithm to directly optimize the stiffness and damping of each of the tuned-mass dampers (TMDs) in such a system. We formulate the parameter optimization as a decentralized H2 control problem where the block-diagonal feedback gain matrix is composed of the stiffness and damping coefficients of the TMDs. The gradient of the root-mean-square response with respect to the design parameters is evaluated explicitly, and the optimization can be carried out efficiently. The effects of the mass distribution, number of dampers, total mass ratio, and uncertainties in system parameters are studied. Numerical results indicate that the optimal designs have neither uniformly spaced tuning frequencies nor identical damping coefficients, and that optimization of the individual parameters in the MTMD system yields a substantial improvement in performance. We also find that the distribution of mass among the TMDs has little impact on the performance of the system provided that the stiffness and damping can be individually optimized.

Damping optimization in mechanical systems with external force

“…Through this section we are going to derive an efficient formula for the functions F s ðvÞ defined as in (15). As we have mentioned in the previous section, first we will assume that the external force is defined as in (16) and that E s j ðvÞ for s ¼ 1; 2 denotes the energy that corresponds to this particular external force.…”

“…Among further we emphasize two books by Chen and Zhen [11,12], where a thorough presentation of techniques and results in this area are given. Some more recent references are [13][14][15] and already mentioned lecture notes [1], where one can find a nice overview of the results connected with viscously damped mechanical systems.…”

Dual Functional Energy Harvesting and Vibration Control: Electromagnetic Resonant Shunt Series Tuned Mass Dampers

“…By employing the Lagrange multiplier method and matrix calculus, the closed form of the gradient @ k H w!z k 2 2 =@F d can be obtained [18,20], as detailed in the Appendix.…”

“…Using matrix calculus, the closed form of the gradient @jjH w!z jj 2 2 =@F d can be obtained [18,20] @jjH w!z jj 2 2…”

Optimal Design of Tuned Mass Dampers by Performance–cost Analysis

“…Similarly the performance of a TMD applied to a multi degree of freedom (MDOF) structure and optimized to control only a single mode of vibration (usually the fundamental one) has been investigated by various authors [24][25]. The optimal parameters of single and multiple TMDs for the control of MDOF structures have been studied by several researchers in the last decades [23,[26][27] also considering the uncertainties affecting structural parameters [28][29]. The above studies mainly take as objective function the efficiency of the TMD expressed by a performance index that generally is chosen as the ratio between the response (displacement, acceleration dissipated energy) of the unprotected system and the same quantity of the protected one.…”